A Resolution of Identity Technique to Speed up TDDFT with Hybrid Functionals: Implementation and Application to the Magic Cluster Series Au 8 n +4 (SC 6 H 5 ) 4 n +8 ( n = 3-6).

The Resolution of Identity (RI) technique has been employed to speed up the use of hybrid exchange-correlation (xc) functionals at the TDDFT level using the Hybrid Diagonal Approximation. The RI has been implemented within the polTDDFT algorithm (a complex damped polarization method) in the AMS/ADF suite of programs. A speedup factor of 30 has been obtained with respect to a previous numerical implementation, albeit with the same level of accuracy. Comparison of TDDFT simulations with the experimental photoabsorption spectra of the cluster series Au 8 n +4 (SR) 4 n +8 ( n = 3-6; R = C 6 H 5 ) showed the excellent accuracy and efficiency of the method. Results were compared with those obtained via the more simplified and computationally cheaper TDDFT+TB and sTDDFT methods. The present method represents an accurate as well as computationally affordable approach to predict photoabsorption spectra of complex species, realizing an optimal compromise between accuracy and computational efficiency, and is suitable for applications to large metal clusters with sizes up to several hundreds of atoms.